Diagram of planar conoprimas
Abstract
The numerous and useful results obtained from the construction of the diagram of spherical conoprimas prompted me to undertake, as a simpler case, the construction of the diagram ofplanar conoprimas. Of course, in both cases the difference is enormous. There we are dealing with the second(-order) of conoprimas; here, only with a prima, since the totality of all similar conoprimas must be regarded as a single entity. In that case, each conoprima is characterized by the angular magnitude of its two axes, which are always real; here, only the principal (major) axis is always real, while the minor axis in the case of hyperbolas is an imaginary axis. The diagram is based on uniting all similar conoprimes into one. But in the composition of hyperbolas there is a striking exception with regard to similarity, namely the limiting case of hyperbolas with equal angles between the asymptotes, that is, the pair of asymptotes themselves, considered as a hyperbola, cannot be said to be similar to all the others. For this reason, the diagram does not include the special hyperbolas consisting of a pair of rays.
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